I am unsure whether this is purely a hardware issue or also software, and in any case usure which sub forum to post in, so at the outset, please direct me to the correct one if I am in the wrong one. Thanks.

I have "inherited" an older mini (says 2006 on the bottom, has 4 USB ports) and want to hook it to a 6 year old Sony Bravia (model KDL-46S3000) 46" 720p TV (has 2 HDMI, two composite, and one DVI [marked RGB?], and an "S Video") in my office. I want to use it mostly for YouTube, concert streaming over the internet, and web surfing via browser. I do not have much experience with Macs, so your patience is appreciated.

The mini has a connector on the video output port on back which converts it to VGA. Should I buy another converter to go directly to the "RGB" port, an HDMI, or to convert the existing VGA output to something else, and what?

How do I get sound to the TV? Each of the above inputs on the TV have either one audio input ("RGB" and Composit) or two (Left and Right) in the case of the HDMI's.

Once all this is done, will my TV function pretty much as a monitor for web browsing, with audio, or are there other issues to solve to accomplish this?

Most Sony TVs have a VGA input for PCs. I think I used that in the past from my Minis. I've used 3 or 4 Sony Tvs with 4 or 5 Minis, never had any probs.
Sorry I can't remember any more specifics.

for audio, the Mini should have an audio out. My 2009 Mini can do digital audio out or analog audio out, both thru the same output depending on the cable used. Not sure if the 2006 Mini had figital but it does have analog audio out. You may need a 1/8" plug for thr Mini ending in L/R audio plugs to your TV input.

Pretty sure it's the RGB port on the TV you want. I think it's actually a VGA that Sony just calls RGB if I remember right. Surely others will chime in. Just study the ports and see what matches.
you can see the S3000 TV manual at Sony.com too to see what Sony says on the ports.

A fully digital connexion should give a better picture and sound.
You will need a DVI-D to HDMI cable and a separate mini-jack to Toslink optical cable for audio (assuming your Sony TV has a Toslink audio input).
Beware however that the Mac Mini 2006 is not really powerful enough (CPU and graphics) to decode/display full HD programs, so you may have pixellisation on such programs.

I would just go with the VGA connection, which is in the PC IN section of the connections(based on the CNET review, and the Sony website). I would recommend against HDMI since you will have to get an adapter, and the Sony might not even accept a computer based HDMI signal, as my Toshiba does not.

Chances are you will have to mess about with SwitchResX in order to get the display to show correct. SwitchResX is really something you will have to mess with to get it right, if you have to use it, since every model of display is different.

Then just a stereo mini-jack from the mini to the display for sound through the Sony's speakers.

As geeji said, it's not gonna have the umph for High Definition content, but the CPU is upgradable. However this upgrade is not to be handled by anyone that is not familiar with the small parts in the mini.